Could you list all of the security models in cryptography?

Question

I only know of some security models:

rom->crs->std

How about others? Or may it be different in several fields?

Thanks.

Answer 1

What you are asking for is not really a list of security models, but more a list of idealized models (like the ROM), and trust assumptions (like the CRS model). Asking for a list seems a bit off-topic to me, and the question is a bit vague.

Anyway, many idealized models and trust models are common in cryptography, and things are in general not as simple as "random oracle model". Here's a non-exhaustive list:

Idealized models:

• The programmable random oracle model (where the simulator can program its output ou inputs of its choice)
• The non-programmable ROM (sometimes used together with a CRS)
• The global ROM (used in the UC model to allow for composition theorems)
• The ideal block cipher model, common in symmetric cryptography
• The quantum ROM, where queries can be in superposition
• The auxiliary-input ROM, which models the fact that a party could have informations hardcoded about a hash function (e.g. a collision)

Trust assumptions:

• The common random string model
• The common reference string model (where the CRS is drawn from some fixed distribution, which is not necessarily uniform)
• The registered key model, a weakening of the previous one, where each player registers some key pair with some authority that it trusts
• The tamper proof hardware token model, where players are given trusted pieces of hardware that can execute some computation

This is just a sample. In general, coming up with an idealized model is a common way to heuristically reason about constructions for which a direct reduction to a hard mathematical problem seems unlikely. While the programmable ROM is very common, there are many alternatives, and also many ways to weaken it, so that it shares more similarities with our "real world" hash functions. Similarly, it is very common also to come up with some minimal trust assumption to get around impossibility results, and while the common random string model is often used, in many scenarios alternative simple trust assumptions can be easily motivated.